Numerical Experience with a Class of Algorithms for Nonlinear Optimization Using Inexact Function and Gradient Information

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. The computational performance of trust region methods for nonlinear optimization is investigated for cases when high accuracy evaluations are unavailable or prohibitively expensive, and earlier theoretical predictions that such methods are convergent even with relative gradient errors of 0.5 or more is confirmed. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.